Paris — Just after most angry French students had toned down their protests to study for exams, disgruntled policemen are challenging the authority of the Socialist government.
President Francois Mitterrand has been forced to dismiss two union leaders, representing about a quarter of the police force. They had organized illegal demonstrations May 3 in the center of Paris after two police officers were killed in the line of duty.
Mr. Mitterrand also suspended seven other top-ranking officers who failed to control the protests, and planned to make a rare appearance on television, reportedly to explain his decisions.
Nevertheless, the police protests promise to remain serious. The dismissed union leaders said they planned to continue their opposition to the government because of its supposed lax law-and-order policies.
In an extreme case, the police could help topple the government. Police dissatisfaction in 1958 with the government's Algeria policy was one cause for the collapse of the Fourth Republic and de Gaulle's return to power.
A more probable outcome, though, is that police dissatisfaction will continue to threaten, but not destroy, the government's authority. The protests so far have been dominated by two right-wing unions, and the majority of the police have not yet joined them.
This tie between the unions and political causes and parties reveals the fundamental problem. Unlike in the United States, law enforcement officials are overtly political in France, and the unions have given political reasons for their protests.
Most policemen have been traditionally conservative. They did not welcome the victory of Francois Mitterrand two years ago. They also did not appreciate what they see as the soft policies of his justice minister, Robert Badinter, who pardoned scores of prisoners, ended the use of the state-security court, and abolished the death penalty.
Only last week did this discontent break into rebellion. At the funeral for the slain policemen, officers shouted down Interior Minister Gaston Defferre and Secretary of State for Public Security Joseph Franceschi.
Later, an extreme right-wing union succeeded in assembling 2,500 off-duty officers for a march to Mr. Badinter's office on the Place Vendome. As the demonstrators marched down rue de Rivoli, the government ordered the other police to stop them, but the on-duty officers let them pass and even took off their hats in support of their colleagues.
In front of Mr. Badinter's office, the policemen shouted, ''Badinter, assassin.'' They then rose their arms in a straight arm salute - the fascist symbol according to Badinter, a victory symbol according to police union leaders - and sang the Marseillaise.
The angry police succeeded in drawing attention to two issues on which the Mitterrand government is vulnerable.
The first is crime. Polls show that after unemployment and inflation, lack of security worries the French the most.
Perhaps more importantly, the police have underscored growing doubts about the competence of the Socialist government. The police demonstrations have accentuated the feeling, conveyed by a whole series of policy flip-flops and public squabbling within the party, that Mr. Mitterrand is not in control.